Question

In projectile motion, the modulus of rate of change of speed.
(a) is constant
(b) first increase then decrease
(c) first decrease then increase
(d) none of the above

Answer 1

Hint – In this question use the concept that speed at any instant is simply the magnitude of instantaneous velocity at that point, so the modulus of rate change of speed is equal to the modulus of the rate of change of velocity w.r.t. time, this will help getting the right answer.

Complete step-by-step answer:

As we know that speed is a scalar quantity (i.e. only magnitude) and velocity is a vector quantity (i.e. magnitude as well as direction).
Now as we know that the speed at any instant is the magnitude of instantaneous velocity that’s why it has only magnitude so, it is a scalar quantity.
And if we take modulus of any vector quantity it becomes scalar quantity.
So the modulus of the rate of change of speed is equal to the modulus of the rate of change of velocity w.r.t. time.
\[ \Rightarrow \left| {\dfrac{{ds}}{{dt}}} \right| = \left| {\dfrac{{dv}}{{dt}}} \right|\]
And we all know that the rate of change of velocity is acceleration.
So in projectile motion the acceleration (a) is working downwards therefore,
$ \Rightarrow a = - g\hat j$, where g = gravity of Earth = 9.8 $m/s^2$.
$ \Rightarrow a = - 9.8\hat j$
Now take the modulus we have,
$ \Rightarrow \left| a \right| = \left| { - 9.8\hat j} \right| = \sqrt {{{\left( { - 9.8} \right)}^2}} = 9.8$
Which is a constant value.
So this is the required answer.
Hence option (A) is the correct answer.

Note – It is advised to know the basic definition of vector and scalar quantities as it helps solving problems of this kind. A vector quantity is one that has both direction as well as magnitude example force, it is generally seen in question statements that a force of 20Kn acts towards the block, and this proves that force is a vector quantity. An entity that has only magnitude and not direction is termed as scalar, example power, energy etc.